Generalizations of de l'Hospital rule

Question

Are there any useful generalizations of de l'Hospital rule? Could you point out some references?

Edit: Something in the spirit of http://arxiv.org/abs/1403.3006, but not necessarily for functions of more that one variable.

Answer 1

Here are a couple of references for certain generalisations:

• L'Hopital's rule for evaluating the limits of complex matrix functions (mapping a matrix to another matrix)

http://www.sciencedirect.com/science/article/pii/S1110256X13000096

• L'Hopital's rule for monotonicity (then used for bounding inequalities of differentiable functions)

http://www.sciencedirect.com/science/article/pii/S0893965908001456

• This document covers various plausible extensions such as discrete analogues (called the Stolz-Cesaro theorem) and summations

http://condor.depaul.edu/mash/LHospitalmmf.pdf

I hope that helps!